The diagram shows part of the curve with equation $$$y=x^{3} \cos 2 x$$$. The curve has a maximum at the point $$$M$$$. Use an iterative formula, based on the equation in part (a), to find the $$$x$$$-coordinate of $$$M$$$ correct to 3 significant figures. Give the result of each iteration to 5 significant figures. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_21 Year：2020 Question No：5(c)

Answer:

Use iteration correctly at least once
Obtain final answer $0.596$
Show sufficient iterations to 5 sf to justify answer or show sign change in interval $[0.5955,0.5965]$

Knowledge points:

2.6.3 understand how a given simple iterative formula of the form relates to the equation being solved, and use a given iteration, or an iteration based on a given rearrangement of an equation, to determine a root to a prescribed degree of accuracy. (Knowledge of the condition for convergence is not included, but an understanding that an iteration may fail to converge is expected.)

Answer:

Knowledge points:

Solution:

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